I'm just beginning to learn Pali using de Silva's primer; I'm on lesson 5. I've begun to develop the habit of reading the first word to ascertain the subject of the sentence and then moving to the last word to get the verb and basically working backwards from there. Is this OK? Will it be good for long term comprehension? How do those of you experienced with reading Pali approach the reading of a sentence? What is your process of dissecting it? Any advice for a rank beginner?

I think any technique is good as long as it allows accurate understanding, but I would give a preference to just reading the words in their order, because that way over time the logic of the language settles in the mind.

Is it possible to become skilled enough at diagramming on pen/paper with diligent practice that it becomes easy to do mentally? And is it clearly worth the effort when compared to just learning mentally/naturally (e.g. if you thought you had good comprehension of Pali but then learned to diagram and got way better, faster, and clearer and you realize that you've been missing out)?

i think what you are doing is a good technique - in the beginning. i teach pali sometimes. i use the same technique to help students to translate pali to english - but only in the beginning. in english the verb comes after the subject. since you are familiar with the sentence structure in english, your method would make you feel more comfortable while translating / learning pali. but to get a feel of the pali language, you can also start reading the pali texts. choose the suttas (translated ones) that you like. then try to read them in pali. your mind will gradually absorb the way the sentences are structured in pali. at the same time continue with your lily de silva book. later you can get grammar books by other authors as well - for cross reference. metta and mudita to you.